Introduction to Demography Ernesto F. L. Amaral March 29, 2016 References: Weeks JR. 2015. Population: An Introduction to Concepts and Issues. 12th edition. Boston: Cengage Learning. Chapters 1 (pp. 1–24), 2 (pp. 25–57). Wachter KW. 2014. Essential Demographic Methods. Cambridge: Harvard University Press. Chapter 1 (pp. 5–29).
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Introduction to Demography
Ernesto F. L. Amaral
March 29, 2016 References: Weeks JR. 2015. Population: An Introduction to Concepts and Issues. 12th edition. Boston: Cengage Learning. Chapters
Rise in life expectancy • Over the past two centuries • Especially since the end of WWII • Most important thing in human history • Consequence and cause of a new way of
viewing the world • Transitions that accompanied it have been
The is the “Ending Logo Slide” layout. It should be the last slide in the deck
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Global population trends (Weeks 2015, Chapter 2, pp. 25–57)
• World population growth – A brief history – How fast is the world’s population growing now? – Power of doubling — How fast can populations grow? – Why was early growth so slow? – Why are more recent increases so rapid? – How many people have ever lived?
• Geographic distribution of world’s population • Global variation in population size and growth
Geographic distribution • Migration flows from rapidly growing areas into
less rapidly growing ones – European expansion: 14th to 20th centuries
• Europe to North and South America and Oceania • Africa to Latin America, Caribbean and North America
– South to North migration: 20th & 21st centuries • Latin America and Asia to the United States • Asia to Canada • Africa, Asia, and Latin America to Europe
Country 2015 Country 2050 1 China 1,402 India 1,620 2 India 1,282 China 1,385 3 United States 325 Nigeria 404 4 Indonesia 256 United States 401 5 Brazil 204 Indonesia 321 6 Pakistan 188 Pakistan 271 7 Nigeria 183 Brazil 231 8 Bangladesh 160 Bangladesh 202 9 Russia 142 Ethiopia 188 10 Japan 127 Philippines 157
Northern Africa and Western Asia • Predominantly Muslim: exception of Israel
– Rapid rates of population growth • Contributing to conflict in the region
– Fertility is declining, but still above death rates • Young populations
• Iran (technically in South Asia) and Turkey – Populous and European-style demographics – Below-replacement fertility, high life expectancy – Southeastern Turkey: high fertility, low female
Growth rate R • Balancing equation for closed population led to
equation for population growth
K(T) = AT K(0)
• B(t)/K(t) and D(t)/K(t) not changing much
• When births exceed deaths, A is bigger than 1 and population increases
• Keeping same value of A through time, we get...
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K(t) with ever-changing slope
Source: Wachter 2014, p. 10.
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Constant slope • Previous graph, we cannot measure growth rate
by graph slope, because it varies – Slope changes even when B/K and D/K are fixed
• We need a measure of growth that stays fixed when B/K and D/K are fixed – Take logarithms of K(t) – Usual way of converting multiplication into addition – log K(t) versus t has constant slope...
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Log K(t) with constant slope
Source: Wachter 2014, p. 10.
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Linear equation • Taking logarithms converts the equation
K(t) = At K(0) • Into the equation
log(K(t)) = log(K(0)) + log(A)t • General form
Y = a +bX • Slope b is log(A), which is called slope R
– Measure of population growth
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Example of slope R
• R = log(1+(B–D)/K) = log(1+(140–57)/6,851)=0.012042 • World population has been growing at a rate of
about 12 per thousand per year since 2000
Population 1 January 2010 6,851 million
+ Births 2010 +140 million
+ Deaths 2010 –57 million
= Population 1 January 2011 6,934 million
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Natural logarithms • We use natural logarithms, which have base
e=2.71828 – “e” is the choice for A that makes the slope of the
graph of K(t) equal 1 when t=0 and K(0)=1
• Population growth rate R – Slope of the graph of the logarithm of population
size over time – Proportional rate of change in population size
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Population growth rate (R) • Ratio of change in vertical axis (rise) to
horizontal axis (run)
• It can also be written as
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Average growth rate • As slope of logarithm of population size
• As proportional rate of change in population size
– When T (interval in years) is close to zero – First factor is ratio of vertical to horizontal axis – Divide it by K(0) to get slope as proportion of size
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Exponential function • Population over time when ratios of births and
deaths to population remain constant
K(t) = At K(0) = eRt K(0) = exp(Rt)K(0)
• Exponential function is the inverse function for natural logarithms
elog(x) = exp(log(x)) = x
log(ey) = log(exp(y)) = y
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Exponential curve • We know that log(A) is R
A = elog(A) = eR
At = (eR)t = eRt = exp(Rt)
• Exponential curve – Graph of exp(Rt) as a function of t – Continuous-time version of the curve for geometric
growth
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Trajectories of exponential growth
Source: Wachter 2014, p. 15.
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Rise and run: China’s log-population
Source: Wachter 2014, p. 15.
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Growth rates in China
Date n “run” R R n
“rise” log(K) K(t)
1960 10 0.0232 0.2320 20.2935 0.651
1970 15 0.0170 0.2550 20.5255 0.821
1985 15 0.0117 0.1755 20.7805 1.059
2000 12 0.0052 0.0624 20.9560 1.262 Source: Census Bureau IDB (2012). Wachter 2014, p. 16.
World population and doubling times Date Population Growth rate Doubling time
8000 B.C. 5 million 0.000489 1417 years 1 A.D. 250 million –0.000373 –1858 years 600 200 million 0.000558 1272 years
1000 250 million 0.001465 473 years 1750 750 million 0.004426 157 years 1815 1,000 million 0.006957 100 years 1950 2,558 million 0.018753 37 years 1975 4,088 million 0.015937 43 years 2000 6,089 million
Source: Estimates drawn from Cohen (1995) and IDB (2012). Wachter 2014, p. 25.
The is the “Ending Logo Slide” layout. It should be the last slide in the deck